Possible applications of the linear sigma model to lattice computations with large M pi.

Using the linear {sigma} model we study the approach to chiral symmetry as the pseudoscalar-meson mass ({ital M}) is varied from {similar to}500 MeV down to the physical value {similar to}{ital M}{sub {pi}}. We show that, even at a tree graph level, the model implies a highly nontrivial dependence of the decay constant ({ital F}{sub {ital M}}), the constituent quark mass ({ital m}{sub {ital q}}), and the scalar ({sigma}) mass ({ital M}{sub {sigma}}) on {ital M}. With an eye to possible applications to {ital K} decays using lattice techniques we examine the relation between {ital K}{r arrow}2{pi}, {ital K}{r arrow} vacuum, and {ital K}{r arrow}{pi} in this approach.